Astronomy educator/Sidewalk astronomer
Owner of Astronomy Delight franchise
18 inch f4.42 Dob on eq platform w ST120 f/5 finder
12 inch Zhumell Dob
8 inch f/6.9 home made Dob with Seevers optics
William Optics red 10th Anniversary 80mm FD
C8 XLT on Vixen GPDX
26lb eyepiece box
Cernan Space Center astronomer
Member of Northwest Suburban Astronomers
20 inch f8 Chief Ed Jones designed and a 17 f9 Zanbuto Wide Band Chief Mike Jones designed .Both unobstructed telescopes .
Quote:Whether it's refraction or reflection, a ray bends at a surface according to good old Snell's law:(Index 1) x sin(A1) = (Index 2) x sin(A2)where angles A1 and A2 are measured away from the 3D perpendicular vector at the surface where the ray intercepts it.The sine of an angle "x" in radians is computed with this series:sin(x) = x - (x^3/3!) + (x^5/5!) - (x^7/7!) + dot dot dotFor small angles, sin(x) = x, and Snell's law becomes (Index 1)(A1) = (Index 2)(A2)Raytracing becomes linear and simple, called "first order" or "paraxial" raytracing. This gives a good approximation where rays would go with no aberrations (other than due to changes in wavelength and index of refraction).Adding in the 3rd order term to sin(x) makes Snell's law(Index 1) [A1 - (A1^3/3!)] = (Index 2) [A2 - (A2^3/3!)]This is called 3rd order optics, and is where spherical aberration, coma, astigmatism and distortion, and variations of these with wavelength, begin to show up. Third order precision is OK for systems with very shallow ray angles and high focal ratios, which is why it was adequate for refractor designing before the days of computers.So you get the idea: 5th order optics includes the x^5/5! term, and so on. The more terms that are included, the more accurately the ray trajectory is calculated. But it reaches a point of ridiculous beyond 5th and 7th order.Then fortunately, along comes 3D skew raytracing and computer implementation in the late 40's, using only square roots that converge rapidly to unbelievable precision, and polynomial analysis becomes obsolete, or at best, of historical curiosity. Aspherics are also easily accomodated by iterative skew tracing. All modern optical programs have 3-D skew raytracing at their heart, but still include 3rd and 5th order aberration outputs if you really have some reason to use them.Simple enough explanation?Mike
Quote: I've been seeing these terms in Suiters book and now Richard Berry's new book and I still don't get what these terms really mean. I suspect 3rd order is general SA and 5th represent zones but I'm not sure.
Quote:One thing I don't understand about that method Vla is that it doesn't account for slope so how does that fit in with refractive index etc?
Scopes & Stuff:
16" F5 Teeter/zambutoTom Osypowski equatorial platform10" F5 LightbridgeMid 70's RV-6Orion 100mm EDATMing:Low Profile Front Collimating Dob/Cell for 16" Conical MirrorFront Collimating Dob/Cell for 16" Standard MirrorDob Driver with novel azimuth friction clutch, and axial (rotating) electrical connection.Red Oak Observing PlatformRed Oak Combination Observing Chair (Post Pending!)
Quote:Perhaps getting back to the spirit of the OPs question, and in addressing my own ignorance of the relevant formalisms, can some rough generalizations be made? That is, can (or perhaps not) some general conclusions be drawn regarding the relative impact on Strehl of nth order vs (n+1)th order aberrations. Similarly for nth-ary vs. (n+1)th-ary aberrations.
Quote: There are two different concepts, that shouldn't be confused. The one is based on using power series of trigonometric functions to simplify the calculation of trigonometric functions back in days when raytracing calculation was done by hand. For most surfaces back then using only the first two terms was sufficiently accurate approximation of trigonometric function. The end (used) term's power was the basis to name the corresponding aberration as "first order", "third order" and so on, as illustrated by the power series posted by Mike.
But this concept is now only of historical significance (think of how much a simple hand calculator would make life easier for the old timers). The concept of aberration order used these days is based on the power series describing conic sagitta. Again, in order to simplify calculation, the sagitta can be described by a power series, with each next term much smaller than the previous. The first term gives exact sagitta for paraboloid; for all other conics additional terms are needed to describe the surface, according to
The second term is the 4th order term, with related aberrations being of 4th order, the next is 6th order, and so on. For other than axial (spherical) aberration, the exponents used are more complex, but it can be simplified to a simple rule that the aberration order is determined by a sum of two exponents: one determining the dependance of wavefront error on zonal height in the pupil, and the other dependance on the field angle.
Primary (or lower-order) spherical changes with the 4th power of zonal height, with zero field angle dependance (4+0), which makes it 4th order
Primary coma changes with the third power of zonal height and in proportion with the field angle (3+1), which also makes it 4th order
Primary astigmatism changes with the square of zonal height and square of the image angle (2+2), so it's 4th order
Secondary (next higher-order spherical) changes with the 6th power of zonal height, with zero field angle dependance (6+0), which makes it 6th order, and so on
These sagitta-related aberrations are wavefront aberrations. Transverse aberrations have the exponent for zonal dependance lower by one, which makes transverse (or ray) primary spherical 3rd order aberration, transverse primary coma 2nd order, and so on.
Likewise, secondary spherical transverse aberration is 5th order, and so on.
Quote:Loren,Strictly talking, we should say 3rd order for the transverse (ray spot) aberration and 4th order for the wavefront. Next higher order are 5th and 6th, respectively, and so on.
Quote:I still don't get it. Thanks all for trying though. And I'm usually pretty good at this stuff...
150mm MCT f/13, 31% CO
"People say I'm in denial. I disagree."
Quote:I disagree; there is no name difference between transverse and wavefront aberrations.
Quote:Piston (the constant term) is considered the zero order term and the next two terms (first and second order) of the expansion form the tilt (linear) and power (r^2) terms. So, the third order terms include spherical aberration, which varies as the fourth power of the radial coordinate in the pupil.
Quote: So even though spherical aberration varies as r^4, it is called “third-order” SA. These third order properties were developed and named by Seidel and (to some extent) Petzval and are what allowed the early development of more sophisticated designs (like achromats.) This approach is still widely used to gain insight into aberration theory and optical properties; though, computer aided design has eliminated the need to consider low order aberrations during the design process.
Quote: I still don't get it.
John Hayes, Ph.D.
Adjunct Research Professor
College of Optical Sciences
University of Arizona
Quote: 1) I am not talking about Zernikes or Wyant’s organization table (which you may be misinterpreting.)
Quote: I am trying to respectfully explain to you that the primary Seidel aberrations are universally called “third-order” for both transverse and wavefront (OPD) formulations. If you walk into a room full of optical engineers (including Wyant who was my dissertation advisor, coauthor, and business partner for 25 years,) they will not know what you are talking about if you refer to primary spherical aberration as “fourth-order spherical.”
Quote: But you don't have to take my word for it. There are all sorts of respected references that make this point: Born and Wolf, "Principles of Optics", 7th edition p232 footnote states: “Since the ray aberrations associated with wave aberrations of this order are of the third degree in the coordinates, they are sometimes called the third order aberrations.” Warren Smith in “Modern Optical Engineering” derives the third order primary Seidels in Chapter 5 and discusses “Third-order” spherical aberration for OPD in Chapter 11. In “Reflecting Telescope Optics, Vol 1, chapter 3.2.2, R.N. Wilson reviews the Seidel Approximation with a derivation of the “third order coefficients” for wavefront aberration. I could give you a lot more references but I’ll stop there.
Quote: This is merely a discussion about the naming of a quantity so it doesn’t matter if you want to call it something different than everyone else, but I feel some obligation to speak up when I see others being told that this is the accepted, correct way to refer to the primary Seidels. It is not.